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Do Now Solve. Course 2 7-8 Populations and Samples 2. n/6 – 9 = 16 Hwk: 65 1. -2N + 20 = 44

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EQ: How do I compare and analyze sampling methods ? Course 2 7-8 Populations and Samples GPS: M7A2a Given a problem define a variable, write an equation, solve the equation, and interpret the solution.

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Vocabulary Population – entire group of objects or individuals considered for a survey Sample – part of a population Random sample – sample in which each individual or object in the entire population has an equal chance of being selected Course 2 7-8 Populations and Samples

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convenience sample – sample based on members of the population that are readily available. biased sample – does not fairly represent the population

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Course 3 Samples and Surveys Sampling Method How Members are Chosen RandomBy chance SystematicAccording to a rule or formula StratifiedAt random from randomly chosen subgroups ConvenienceEasiest to reach Voluntary- response Members choose to be in the sample

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In 2002, there were claims that Chronic Wasting Disease (CWD), or Mad Elk Disease, was spreading westward across North America. In order to verify claims such as these, the elk population had to be tested. When information is gathered about a group, such as the elk in North America, the entire group is called the population. Because testing each member of a large group can be difficult or impossible, researchers often study a part of the population, called a sample. Course 2 7-8 Populations and Samples

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Course 2 7-8 Populations and Samples For a random sample, members of the population are chosen at random. This gives every member of the population an equal chance of being chosen. A convenience sample is based on members of the population that are readily available, such as 30 elk in a wildlife preservation area. A random sample is more likely to be representative of a population than a convenience sample is. Helpful Hint

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Determine which sampling method will better represent the entire population. Justify your answer. Additional Example 1: Analyzing Sampling Methods Course 2 7-8 Populations and Samples Sampling method Maria surveys only the band students she knows personally. Results 84% want blue uniforms Jon writes each band students name on a card. He questions those students whose name he draws. 61% want blue uniforms Jons sample is a random sample, giving every band member equal chance to be surveyed, so it is the better method.

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Determine which sampling method will better represent the entire population. Justify your answer. Check It Out: Example 1 Course 2 7-8 Populations and Samples Sampling method Ferdinand surveys every other swimmer on the team. Results 72% want practice early Anna-Maria questions the swimmers who are in her Biology class. 50% want practice early Ferdinands sample is a random sample, giving results that better represent the entire swimming team, so it is the better method.

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Course 3 9-1 Samples and Surveys Additional Example 1A: Identifying Sampling Methods Identify the sampling method used. In a county survey, Democratic Party members whose names begin with the letter D are chosen. systematic The rule is to survey members whose names begin with D.

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Course 3 9-1 Samples and Surveys A telephone company randomly chooses customers to survey about its service. random Customers are chosen by chance. Additional Example 1B: Identifying Sampling Methods Identify the sampling method used.

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Course 3 9-1 Samples and Surveys A high school randomly chooses three classes from each grade and then draws three random names from each class to poll about lunch menus. stratified The three classes are the random subgroups. Names are chosen randomly from within the classes. Additional Example 1C: Identifying Sampling Methods Identify the sampling method used.

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Course 3 9-1 Samples and Surveys Check It Out: Example 1A Identify the sampling method used. In a county survey, families with 3 or more children are chosen. systematic The rule is to survey families with 3 or more children.

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Course 3 9-1 Samples and Surveys Check It Out: Example 1A Identify the sampling method used. In a county survey, families with 3 or more children are chosen. systematic The rule is to survey families with 3 or more children.

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Course 3 9-1 Samples and Surveys Check It Out: Example 1A Identify the sampling method used. In a county survey, families with 3 or more children are chosen. systematic The rule is to survey families with 3 or more children.

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A biased sample does not fairly represent the population. A study of 50 elk belonging to a breeder could be biased because the breeders elk might be less likely to have Mad Elk Disease than elk in the wild. Course 2 7-8 Populations and Samples

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Determine whether each sample may be biased. Explain. Additional Example 2: Identifying Potentially Biased Samples A. The mayor surveys 100 supporters at a rally about the most important issues to be addressed by the city council. Course 2 7-8 Populations and Samples The sample is biased. The supporters may have different ideas than those not at the rally. B. The principal sends out questionnaires to all of the students to find out what kind of music students prefer at dances. The sample is random. The students all have a chance to respond.

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Determine whether each sample may be biased. Explain. Check It Out: Example 2 Course 2 7-8 Populations and Samples A. The owner of a record shop surveys only customers over the age of 18 who shop at his store. This is not random. Customers under the age of 18 do not have a chance of being chosen. B. The teacher writes the name of each student on a piece of paper and questions the students whose names are drawn. This sampling method is random. Each student has an equal chance of being chosen.

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Course 3 Samples and Surveys People attending a baseball game were asked if they support the construction of a new stadium in the city. City residents People attending a game People that attend a baseball game are more likely to support the construction of a new stadium. Check It Out: Example 2C Identify the population and the sample. Give a reason why the sample could be biased. PopulationSamplePossible Bias

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Course 3 9-1 Samples and Surveys Eighth-grade students with a 3.0 GPA or higher were polled to determine how long students study each day. Eighth grade students Students with 3.0 or higher GPA Students with lower grades are less likely to study as long. Check It Out: Example 2B Identify the population and the sample. Give a reason why the sample could be biased. PopulationSamplePossible Bias

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Course 3 9-1 Samples and Surveys Check It Out: Example 2A The first 5 people leaving a movie theater at a sneak preview were asked how they liked the movie. People that went to the movie The first five people that left People that really enjoy a movie are less likely to be one of the first ones to leave. PopulationSamplePossible Bias Identify the population and the sample. Give a reason why the sample could be biased.

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A principal of a school with 1,500 students estimates that about 400 students will attend a band festival on Saturday. A random sample of 25 students showed that 6 of them will attend. Determine whether the principals estimate is likely to be accurate. Additional Example 3: Verifying Claims Based on Statistical Data Course 2 7-8 Populations and Samples Set up a proportion to predict the total number of students that will attend. Students attending sample # of Students sampled Students attending Student Population =

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Additional Example 3 Continued Course 2 7-8 Populations and Samples 6 25 x 1500 = 360 = x The estimate is not accurate because the data shows that 360 students are likely to attend.

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The owner of a large chain restaurant with 1,200 employees estimates that about 250 employees will ask for winter vacation. A random sample of 40 employees showed that 8 of them will ask for the time off. Determine whether the owners estimate is likely to be accurate. Check It Out: Example 3 Course 2 7-8 Populations and Samples Set up a proportion to predict the total number of students that will attend. Employees surveyed for time off # of Employees surveyed Employees asking for time off Total # of Employees =

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Check It Out: Example 3 Continued Course 2 7-8 Populations and Samples 8 40 x 1200 = 240 = x The estimate is accurate because the data shows that 240 employees will ask for time off.

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a. A TV ratings service is surveying residents of Orlando who bought TVs in the last month about their favorite TV show. b. A TV ratings service called residents of Orlando randomly selected from the phone directory to conduct a survey about their favorite show. TOTD Course 2 7-8 Populations and Samples b 1. Determine which sample better represents the entire population.

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2. Determine whether each sample may be biased. Explain. TOTD Course 2 7-8 Populations and Samples Biased; at other times of the day, customers may have different preferences. a. A convenience store surveys customers one morning to determine what products they may like the store to stock. b. Each students name is written on a slip of paper and placed in a box. One slip of paper is selected to determine the student to be the homeroom representative. Not biased; the sample is random.

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3. A local middle school has 2500 students. Morgan interviewed 75 of the students about their library habits. She found that 45 of the students checked out a book weekly. Predict the number of students likely to check out books weekly. TOTD Course 2 7-8 Populations and Samples 1500

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